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Simulating the Flow of Liquid Droplets

Patrick Fournier, Arash Habibi, and Pierre Poulin
Proc. Graphics Interface 98, June 1998


The ever-changing nature of liquids makes them very difficult to model and animate. This paper addresses the simulation of one aspect of liquids, i.e. droplets running down surfaces. We present a model oriented towards a visually-satisfying simulation and efficiency.

The efficiency results from the separation between the shape and the motion of a droplet. The motion accounts for all changes encountered along the path followed over a mesh of triangles. It is affected by various properties modeled as friction, adhesion, roughness, and collisions between droplets. Streaks are also added along the paths.

We characterize the shape of a droplet by a small set of properties, such as volume conservation, surface tension, etc. We model them as constraints to satisfy. The shape model is mainly based on mass-springs. It is simple and efficient, and it guarantees that whatever the values of the unconstrained parameters, all produced shapes satisfy the characteristic properties, and thus, can represent different types of droplets.

Rendered animations of various liquids illustrate the resulting simulation.

BibTeX entry


Online Version

Postscript available here

Related work

on various proofs developed for the original paper appear in the following document.

A Study of the Static Properties of a Mass-spring network with a Spider-web Topology by Arash Habibi.

Images related to the paper

The same drolet shape, but changing the light direction from grazing to about 45 degrees. Notice the light distribution on the base within the droplet going from sharper to most diffuse. This light distribution comes from textures capturing the illumination at the base of a half-sphere, and mapped to the shape of the droplet. The polygonal nature of the droplet surface is visible by the discontinuities in the highlight region. A finer mesh subdivision of the underlying spline representation would reduce this artifact.